World Cup Women U17 Final Stages stats & predictions

Overview of the U17 Women's World Cup Final Stages

The U17 Women's World Cup is reaching its thrilling final stages, where teams from around the globe compete for the coveted title. This tournament showcases young talent and provides a platform for emerging stars to shine on the international stage. As we look ahead to tomorrow's matches, anticipation builds among fans and analysts alike.

Key Teams in the Final Stages

• Team A: Known for their tactical prowess and strong defense, Team A has consistently demonstrated their ability to control games and capitalize on scoring opportunities.
• Team B: With a focus on speed and agility, Team B has been impressive in their offensive play, making them a formidable opponent.
• Team C: Renowned for their resilience and teamwork, Team C has shown remarkable improvement throughout the tournament.
• Team D: With a balanced squad that excels in both attack and defense, Team D remains one of the favorites to win.

Tactical Analysis

As teams prepare for tomorrow's matches, understanding their tactics becomes crucial. Each team brings unique strengths to the field:

• Tactic 1: Defensive Solidity - Teams like Team A rely on a strong defensive line to thwart opponents' attacks while looking for counter-attacking opportunities.
• Tactic 2: High Pressing Game - Teams such as Team B use high pressing to regain possession quickly and launch rapid attacks.
• Tactic 3: Possession Play - Teams like Team C focus on maintaining possession to control the tempo of the game and patiently break down defenses.
• Tactic 4: Balanced Approach - Teams such as Team D employ a balanced strategy, adapting their play style based on the opponent's strengths and weaknesses.

Prediction Models & Betting Insights

The excitement surrounding tomorrow’s matches extends beyond just sports enthusiasts; it also captivates betting analysts who provide expert predictions based on comprehensive data analysis. Here are some insights into what might unfold:

1. Betting Odds Analysis: Current odds suggest that Team A has a slight edge due to their consistent performance throughout the tournament. However, betting markets remain volatile as underdogs like Team C could upset expectations with strategic plays.
2. Prediction Models: Advanced prediction models consider various factors such as historical performance, player form, weather conditions, and tactical matchups. These models indicate that while Team A is favored, close attention should be paid to potential upsets from teams with strong attacking capabilities like Team B.
3. Betting Strategies: For those interested in placing bets, considering value bets where odds may not fully reflect potential outcomes can be advantageous. Additionally, analyzing live betting markets during matches can provide opportunities based on real-time developments.
4. Risk Management: It’s essential for bettors to manage risks by setting limits on stakes and diversifying bets across different outcomes rather than focusing solely on outright winners or losers.

Detailed Match Predictions

The following predictions are based on current trends and expert analyses leading up to tomorrow’s fixtures:

• Match Prediction: Team A vs. Team B
  The clash between two top contenders promises an intense battle. While both teams have shown exceptional skills throughout this tournament:
  • Prediction Outcome: The match is expected to end in a draw with both teams likely sharing points due to evenly matched skill levels and tactical approaches.
  • Key Players: Watch out for Player X from Team A known for her strategic vision; Player Y from Team B renowned for speed will also be crucial.
  • Betting Tip:: Consider backing over/under goals market given both teams' defensive capabilities.
  
  
  
  
• Match Prediction: Team C vs. Team D
  This matchup pits two contrasting styles against each other—Team C's resilience against Team D's balance.
  • Prediction Outcome:: Although favored slightly by bookmakers due to recent performances at home grounds; expect surprises as underdogs often rise when least expected.
  • Key Players:: Keep an eye out for Player Z from team C whose tenacity could turn tides; meanwhile watch how Player W adapts his game plan against dynamic oppositions.
  • Betting Tip:: Place your bets cautiously but consider taking advantage of live odds adjustments during critical moments within these tightly contested fixtures.
  
  
  
  

  Influence of External Factors

  In addition to tactical preparations by coaches and players’ performances under pressure situations during past games contributing significantly towards shaping these predictions further external elements play pivotal roles including weather conditions prevailing at venues hosting respective fixtures or unexpected injuries affecting lineup choices which could potentially alter predicted outcomes substantially affecting stakeholder decisions whether they’re fans cheering passionately or punters seeking lucrative returns through strategic wagers placed judiciously upon informed assessments derived analytically encompassing multifaceted aspects influencing football dynamics globally witnessed prominently today especially amidst high-stakes tournaments such as this one being discussed here presently involving upcoming elite-level competitions featuring promising young talents striving earnestly toward achieving remarkable feats destined possibly shaping future trajectories within women’s football landscape worldwide soon enough!

  Social Media Buzz & Fan Engagement Strategies

  The build-up towards tomorrow’s matches isn’t limited just within stadiums or betting circles but extends across social media platforms where fan engagement strategies are leveraged extensively by clubs & sponsors alike aiming at amplifying viewership numbers thereby increasing brand visibility alongside generating additional revenue streams through advertising partnerships effectively capitalizing upon heightened public interest surrounding these pivotal encounters between world-class young athletes representing diverse nations vying passionately striving collectively individually endeavoring together towards shared aspirations manifesting vividly through captivating narratives unfolding dynamically across screens large small everywhere imaginable anywhere conceivable during globally celebrated events akin currently ongoing U17 Women’s World Cup Final Stages International Tomorrow! Engage actively participate share opinions debate heatedly discuss fervently express emotions passionately cherish every moment eagerly awaiting eagerly anticipating eagerly anticipating eagerly anticipating eagerly anticipating eagerly anticipating eagerly anticipating eagerly awaiting these monumental occasions set forth ahead filled brimming overflowing exhilaration excitement anticipation joyous celebrations communal spirit unity transcending boundaries borders borders borders borders borders borders!

  Economic Impact & Sponsorship Opportunities

  The economic ramifications associated with hosting major sporting events like this extend far beyond ticket sales alone encompassing multiple sectors including hospitality tourism transportation local businesses all experiencing surges demand consequently boosting overall economic activity significantly benefiting communities involved hosting such prestigious tournaments additionally attracting lucrative sponsorship deals providing brands unparalleled exposure reach global audiences thus presenting invaluable marketing opportunities fostering mutually beneficial partnerships enhancing brand visibility reputation simultaneously promoting sports development initiatives aimed improving infrastructure facilities nurturing grassroots programs empowering aspiring athletes worldwide ensuring sustained growth progression sustainable future prospects football particularly women’s football promising bright horizon filled endless possibilities awaiting exploration discovery innovation creativity collaboration cooperation collective efforts committed stakeholders dedicated mission advancing sport excellence inclusivity diversity equality empowerment inspiring generations forthcoming!

  Cultural Significance & Legacy Building Efforts

  The significance of events like these transcends mere athletic competition encompassing broader cultural dimensions fostering cross-cultural exchanges promoting understanding tolerance respect diversity uniting people irrespective geographical differences backgrounds ideologies coming together celebrating shared love passion common humanity collectively appreciating achievements triumphs overcoming adversities challenges encountered along journey thus leaving indelible marks legacies inspiring future generations aspiring emulate footsteps predecessors paving paths forward embracing values principles integrity honesty perseverance determination resilience courage compassion empathy kindness humility gratitude hope optimism peace harmony solidarity unity strength love cherished forever cherished forever cherished forever cherished forever cherished forever cherished forever cherished forever cherished forever cherished forever cherished forever onwards! <|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep|>/_posts/2020-04-22-why-we-use-a-wireframe.md --- layout: post title: Why We Use Wireframes? date: '2020-04-22' permalink: /why-we-use-a-wireframe/ tags: - UX Design --- In this post I will explain why wireframes are important part of UX design process. # What is Wireframe? A wireframe is basically a visual guide that represents skeletal framework of website pages.  Wireframes can be used early in project lifecycle when you want validate idea before you start building something costly. # Benefits of Wireframing ## Helps Us Understand User Needs When you create wireframes you start thinking about user needs because you need understand what users want achieve using website/app before creating anything else. For example if someone wants buy product online then they probably want find product easily add it cart checkout quickly without any hassle right? So when designing e-commerce site first thing come mind would probably make sure users can do exactly those things easily right? And that’s exactly what wireframing helps us do! ## Makes Us Focus On Content Not Design Elements One problem many designers face when starting new project is getting distracted by all different design elements available today (colors fonts images animations etc.). But if we focus too much attention details then we might forget main purpose our project which should always be providing best possible experience users! So instead spending hours deciding which color scheme looks better let’s spend time thinking about content structure layout navigation etc., because those things matter most! ## Saves Time And Money Another benefit using wireframes early stage development process saving both time money later down road because once everything planned out properly there won’t need change anything drastic later which means less work rework redesign etc. # Conclusion So next time someone ask “Why do we need wireframes?” just tell them it helps us understand user needs makes us focus content not design elements saves time money later down road! That being said there still some situations where skipping wireframing completely might make sense depending project requirements budget timeline etc., but generally speaking unless there specific reason otherwise creating wireframes should definitely part every designer toolkit!<|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep [](https://travis-ci.org/benoitdavid12/benoitdavid12.github.io) [](https://app.netlify.com/sites/clever-hodgkin-eefb67/deploys) My personal blog powered by Jekyll. ### How To Run Locally bash $ bundle install --path vendor/bundle $ bundle exec jekyll serve --incremental --livereload ### How To Deploy Locally bash $ bundle exec jekyll build && netlify deploy --dir _site --prod <|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep passing through an area where there are no obstacles or hazards. Here are some synonyms: 1. Unobstructed passage 2. Clear path 3. Open route 4. Unimpeded travel 5. Safe passage These terms convey similar meanings related to moving through an area without interference or danger.<|file_sep publicity campaign? In order words publicity campaign is way companies promote products services brands themselves using various media channels reach target audience increase awareness generate interest sales ultimately achieve desired objectives.<|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep**SEO Expert Text** The U17 Women's World Cup final stages present an exciting opportunity for fans around the world as they witness young talents competing at an international level. This event not only highlights emerging soccer stars but also offers intriguing possibilities in terms of betting predictions due to its unpredictable nature. As we approach tomorrow's matches in this prestigious tournament held annually since its inception in [Year], several key factors come into play when considering expert betting tips: 1) **Current Form**: Assessing each team's recent performances provides insight into their likelihood of success during upcoming games. 2) **Head-to-head Statistics**: Historical data regarding previous encounters between participating squads can influence betting odds significantly – especially if certain patterns emerge over time (e.g., dominance by one side). 3) **Injury Reports**: Updates concerning player availability may drastically affect team dynamics; thus impacting potential outcomes within individual fixtures. With these considerations in mind along with thorough analysis provided by seasoned analysts across various platforms offering expert advice tailored specifically towards football enthusiasts seeking reliable guidance while placing wagers – let us delve deeper into predicting possible results stemming from tomorrow's action-packed schedule: **Match Predictions** * **Team A vs. Team B** * **Analysis**: Both squads boast impressive records throughout earlier rounds showcasing formidable offensive capabilities complemented by solid defensive structures making them top contenders within Group Stage standings respectively * **Expert Tip**: Expect closely contested encounter where goals scored will likely dictate victor favorability leans slightly towards stronger attacking prowess displayed historically suggesting slight edge lies here though unpredictability remains high given youthful exuberance present throughout entire roster composition * **Team C vs. D** * **Analysis**: Known more defensively oriented strategy contrasted starkly against aggressive forward line capable exploiting vulnerabilities left open behind * **Expert Tip**: Likely outcome sees narrow victory margin potentially influenced heavily physicality aspect present pitch dynamics dictating pace flow overall result hinges largely midfield battles control possession crucial determining factor here * **E vs F** * **Analysis**: Recent form suggests momentum swings wildly mid-tournament period necessitating careful scrutiny player fitness levels injury concerns pivotal aspects shaping expectations * **Expert Tip**: Expect tight affair where defensive solidity coupled with opportunistic striking spells decisive moments tipping scales either direction depending execution executed key phases match progression **Betting Insights** When placing bets regarding upcoming fixtures several strategies merit consideration: 1) **Over/Under Goals Market** – Given unpredictability nature youth tournaments opting conservative approach might yield favorable returns focusing goal tallies rather than outright winner selections allows capitalizing fluctuations match intensity variability inherent format itself. 2) **Draw No Bet** – Offering protection against unforeseen tie scenarios enables wager placement confidence level higher reducing risk exposure while maximizing potential rewards especially prevalent tightly contested fixtures featuring evenly matched adversaries commonly observed latter stages competitive environments such as U17 World Cups. 3) **Asian Handicap Lines** – Utilizing handicaps effectively balances perceived disparities strength advantages facilitating more equitable betting propositions encouraging engagement broader audience spectrum regardless individual expertise levels ensuring fairer chances success participation wager activities centered around anticipated match outcomes accordingly adjusted parameters align respective expectations reality situationally presented circumstances unfold progressively evolving narrative arc unfolding live spectacles unfolding stadium confines globally broadcast digital mediums alike engross vast audiences enthralled captivating drama encapsulating essence sport spectacle collective human endeavor pursuit excellence passion camaraderie unity transcending boundaries barriers language cultural divides universally understood language love admiration reverence admiration awe wonderment amazement awe-inspiring displays athleticism skill dedication perseverance commitment unwavering determination indomitable spirit triumph adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity adversity.<|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep incurs legal consequences if someone steals your personal information without your consent?<|file_sep): # Personal Website using Jekyll theme Minimal Mistakes Minimal Mistakes is a responsive Jekyll theme designed after working through my own frustrations with other themes available out there. It was developed using Jekyll version `v4`. This theme uses Bootstrap v5 so if you would like information about Bootstrap see [here](https://getbootstrap.com/docs/5/0/getting-started/introduction/) <|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep checkpoint? A checkpoint refers point along route path designated specific purpose monitoring progress ensuring adherence predetermined standards regulations guidelines established authority overseeing operation task completion journey voyage mission expedition endeavor undertaking quest adventure exploration discovery pursuit achievement accomplishment fulfillment satisfaction realization aspiration ambition desire dream vision objective goal aim intention target aspiration ambition desire dream vision objective goal aim intention target.<|repo_name|>benoitdavid12/benoitdavid12.github.io<|file_sep1); //if ((rand() % (100)) <= chanceOfLightning) if ((rand() % (100)) <= chanceOfLightning) { if (!lightningBolt->IsEnabled()) lightningBolt->Enable(); else lightningBolt->Disable(); isLightningActive = !isLightningActive; return true; } return false; } bool IsLightningActive() { return isLightningActive; } void SetChanceOfLightning(int newChanceOfLightning) { chanceOfLightning = newChanceOfLightning; } private: bool IsRainyWeather() { return rainEffect->IsEnabled(); } private: RainEffect* rainEffect; LightningBolt* lightningBolt; int chanceOfLightning; bool isRainyWeather; bool isThunderStorm; bool isLightningActive; }; // end class WeatherManager class WaterEffect : public SceneObject { public: WaterEffect(int sceneWidth, int sceneHeight, std::string name, glm::vec2 position, glm::vec2 scale, float rotation, glm::vec4 color); virtual void Update(float deltaTime); virtual void Render(); private: int width; int height; unsigned int textureID; }; // end class WaterEffect WaterEffect::WaterEffect(int sceneWidth, int sceneHeight, std::string name, glm::vec2 position, glm::vec2 scale, float rotation, glm::vec4 color) { this->name = name; this->position = position; this->scale = scale; this->rotation = rotation; this->color = color; width = sceneWidth / WATER_PARTICLE_SIZE_DIVISOR_X + WATER_PARTICLE_SIZE_DIVISOR_X - PADDING_X_MULTIPLIER * PADDING_X_DIVISOR_X; height = sceneHeight / WATER_PARTICLE_SIZE_DIVISOR_Y + WATER_PARTICLE_SIZE_DIVISOR_Y - PADDING_Y_MULTIPLIER * PADDING_Y_DIVISOR_Y; textureID = LoadTexture("assets/textures/water.png"); CreateVertexArray(width,height); } void WaterEffect::Update(float deltaTime) { for (int y = yStartIndex; y <= yEndIndex; ++y) for (int x = xStartIndex; x <= xEndIndex; ++x) if (!particles[x][y].active) for (int i = PARTICLE_START_INDEX; i <= PARTICLE_END_INDEX; ++i) if (!particles[x][y].particles[i].active) if ((rand() % (100)) <= CHANCE_OF_SPAWN_WATER_PARTICLES_PER_FRAME_IN_PERCENTS) if (particleSpawnCooldownFrames == PARTICLE_SPAWN_COOLDOWN_FRAMES_BEFORE_WATER_SPAWNING_IN_FRAMES || particleSpawnCooldownFrames == -1) if (!waterParticleSpawnTimer.IsRunning()) { particles[x][y].particles[i].position.x = particles[x][y].position.x + PARTICLE_OFFSET_FROM_CENTER_TO_TOP_LEFT_CORNER_IN_PIXELS + static_cast(rand() % PARTICLE_SIZE_IN_PIXELS); particles[x][y].particles[i].position.y = particles[x][y].position.y + PARTICLE_OFFSET_FROM_CENTER_TO_TOP_LEFT_CORNER_IN_PIXELS + static_cast(rand() % PARTICLE_SIZE_IN_PIXELS); particles[x][y].particles[i].color.r = static_cast((rand() % COLOR_VARIATION_RANGE + MIN_COLOR_VALUE)); particles[x][y].particles[i].color.g = static_cast((rand() % COLOR_VARIATION_RANGE + MIN_COLOR_VALUE)); particles[x][y].particles[i].color.b = static_cast((rand() % COLOR_VARIATION_RANGE + MIN_COLOR_VALUE)); particles[x][y].particles[i].color.a = MAX_COLOR_VALUE; particles[x][y].particles[i].size.x = static_cast(PARTICLE_MIN_SIZE_IN_PIXELS + static_cast(static_cast(PARTICLE_MAX_SIZE_DIFFERENCE_IN_PIXELS) * randDouble())); particles[x][y].particles[i].size.y = static_cast(PARTICLE_MIN_SIZE_IN_PIXELS + static_cast(static_cast(PARTICLE_MAX_SIZE_DIFFERENCE_IN_PIXELS) * randDouble())); particles[x][y].active++; break; } // end if active particles count check waterParticleSpawnTimer.Start(); waterParticleSpawnTimer.SetInterval(PARTICLE_SPAWN_INTERVAL_BETWEEN_WAVEFRONTS_IN_SECONDS); break; waterParticleSpawnTimer.Update(deltaTime); waterParticleSpawnCooldownFrames--; break; waterParticleSpawnCooldownFrames--; break; waterParticleSpawnCooldownFrames--; break; waterParticleSpawnCooldownFrames--; break; } void WaterEffect::Render() { glBindVertexArray(VAO); glBindTexture(GL_TEXTURE_2D,textures[textureID]); GLfloat vertices[]= { glGetAttribLocation(shaderProgram,"vertexPosition_modelspace"), glVertexAttribPointer(0,//location DIMENSIONS,//componentsPerAttribute GL_FLOAT,//type GL_FALSE,//normalized sizeof(Vertex)//stride NULL);//pointer glGetAttribLocation(shaderProgram,"vertexColor"), glVertexAttribPointer(1,//location DIMENSIONS,//componentsPerAttribute GL_FLOAT,//type GL_FALSE,//normalized sizeof(Vertex)//stride NULL);//pointer glGetAttribLocation(shaderProgram,"texCoord"), glVertexAttribPointer(2,//location DIMENSIONS,//componentsPerAttribute GL_FLOAT,//type GL_FALSE,//normalized sizeof(Vertex)//stride NULL);//pointer glEnableVertexAttribArray(0);//enable vertexPosition_modelspace attribute array glEnableVertexAttribArray(1);//enable vertexColor attribute array glEnableVertexAttribArray(2);//enable texCoord attribute array for(int y=yStartIndex;y<=yEndIndex;++y){ for(int x=xStartIndex;x<=xEndIndex;++x){ for(int i=PARTICLE_START_INDEX;i<=PARTICLE_END_INDEX;++i){ if(particles[x][y]. active==true&& particles[x] y.particles[i]. active==true){ glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"MVP"),//MVP location GL_FALSE,//transpose NULL,&MVP);//matrix glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"MV"),//MV location GL_FALSE,//transpose NULL,&MV);//matrix glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"P"),//P location GL_FALSE,//transpose NULL,&P);//matrix glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"model"),//model location GL_FALSE,//transpose NULL,&model);//matrix glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"modelInverseTranspose"),//modelInverseTranspose location GL_FALSE,//transpose NULL,&modelInverseTranspose);//matrix glUniformMatrix4fv(glGetUniformLocation(shaderProgram,"normalMatrix"),//normalMatrix location GL_FALSE,//transpose NULL,&normalMatrix);//matrix glUniform1i(glGetUniformLocation(shaderProgram,"textureSampler"),//textureSampler location TEXTURE_UNIT_0); glUniform1f(glGetUniformLocation(shaderProgram,"timeSinceStartInSeconds"),timeSinceStartInSeconds); glUniform1f(glGetUniformLocation(shaderProgram,"currentTimeInSeconds"),currentTimeInSeconds); glUniform1f(glGetUniformLocation(shaderProgram,"deltaTimeInSeconds"),deltaTimeInSeconds); glUniform3f(glGetUniformLocation(shaderProgram,"cameraPosition_worldspace"), cameraPosition_worldspace.x, cameraPosition_worldspace.y, cameraPosition_worldspace.z); glUniform3f(glGetUniformLocation(shaderProgram,"sunDirection_worldspace"), sunDirection_worldspace.x, sunDirection_worldspace.y, sunDirection_worldspace.z); glUniform3f(glGetUniformLocation( shaderprogram, "sunColor"), static_cast< GLfloat>( particles[ x] [ y]. particles[ i]. color.r), static_cast< GLfloat>( particles[ x] [ y]. particles[ i]. color.g), static_cast< GLfloat>( particles[ x] [ y]. particles[ i]. color.b)); glUniform3f( glGetUniformLocation( shaderprogram, "lightPosition_worldspace"), static_cast< GLfloat>( lightPosition_worldspace.x), static_cast< GLfloat>( lightPosition_worldspace.y), static_cast< GLfloat>( lightPosition_worldspace.z)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "materialAmbientColor"), glm:: value_ptr(materialAmbientColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "materialDiffuseColor"), glm:: value_ptr(materialDiffuseColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "materialSpecularColor"), glm:: value_ptr(materialSpecularColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "materialShininessFactor"), glm:: value_ptr(materialShininessFactor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "lightAmbientColor"), glm:: value_ptr(lightAmbientColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "lightDiffuseColor"), glm:: value_ptr(lightDiffuseColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "lightSpecularColor"), glm:: value_ptr(lightSpecularColor)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "eyePointWorldSpace"), glm:: value_ptr(cameraPosition_worldspace)); glUniformFloatArray( glGetUniformLocation( shaderprogram, "pointSize"), glm:: value_ptr(pointSize)); glBindBuffer(GL_ARRAY_BUFFER,buffers[bufferIndices[bufferIndex]]); glBufferData(GL_ARRAY_BUFFER,sizeof(particleVertices)*particleVertices.size(), &particleVertices.front(),GL_STATIC_DRAW); glDrawArrays(GL_POINTS,PARTICLES_PER_QUAD*i,PARTICLES_PER_QUAD); glBindBuffer(GL_ARRAY_BUFFER,NULL); particleVertices.clear(); model=modelIdentity; model=glm:: translate(model,pow(-x,y,-z)); model=glm:: rotate(model,radians(rotation),glm:: vec3(0.f,-90.f,-180.f)); model=glm:: scale(model,scale.x,scale.y,scale.z); model=glm:: translate(model,-scale.x*scale.x,-scale.y*scale.y,-scale.z*scale.z); model=glm:: translate(model,pow(x,y,z)); modelView=model*view; M=modelView*perspectiveProjection; MV=modelView; normalMatrix=glm:: transpose(glm:: inverse(glm:: mat3(M))); particleVertices.push_back(Vertex(glm:: vec3(particles[ x] [ y]. particles[ i]. position.x-pow(-x,y,-z).x+pow(x,y,z).x-sunOffset_x,particles[ x] [ y]. particles[ i]. position.y-pow(-x,y,-z).y+pow(x,y,z).y-sunOffset_y,particles[ x] [ y]. particles[ i]. position.z-pow(-x,y,-z).z+pow(x,y,z).z-sunOffset_z),glM:: vec2(particles[ x] [ y]. particles[ i]. size.x/particleSizeDivisor_x,particles[ x] [ y]. particles[ i]. size.y/particleSizeDivisor_y),glM:: vec4(particles[ x] [ y]. particles[ i]. color.r,particles[ x] [ arXiv identifier: hep-ph/9504266 DOI: 10.1016/0370-2693(95)00639-D # Radiative Corrections at Thresholds of Heavy Flavors Production Revisited I : $tbar{t}$ Thresholds Near $m_t sim m_Z$ Authors: S.P.Kovalevskyi(Ukrainian Natl.Univ.), E.A.Kuraev(Institute N.N.Bogolyubov), G.P.Sidorov(Institute N.N.Bogolyubov), V.V.Yakovenko(Institute N.N.Bogolyubov), V.M.Zakharov(Institute N.N.Bogolyubov), Yu.L.Dokshitzer(LPTHE-Saclay). Date: 28 October 2009 Categories: hep-ph hep-th nucl-th ## Abstract We calculate radiative corrections near thresholds $m_t sim m_Z$ assuming $m_bll m_t$. In particular we consider QCD corrections $alpha_s^k$ ($kgeqslant{}1$ )and electroweak ones $alpha_{ew}^l$, ($lgeqslant{}1$ ). We show that contributions proportional $ln^k(m_t/m_Z)$ $(kgeqslant{}l+1)$ vanish at each order $O(alpha_s^k alpha_{ew}^l)$ . Using this fact we construct complete expressions which include all logarithmic terms $ln^n(m_t/m_Z)$ ($nleqslant{}l$ )at each order $O(alpha_s^k alpha_{ew}^l)$ . We show that large logarithms $ln^n(m_t/m_Z)$ $(nleqslant{}l)$ , coming from virtual QCD corrections give negligible contribution near threshold regions ($m_t sim{}m_Z$ ). Thus they do not spoil perturbative expansion even at threshold regions . ${}^*$ Permanent address : Institute for Nuclear Researches , National Academy Of Sciences , Ukraine , G.Skovoroda Str., L’viv , UA–61103 , Ukraine . ${}^{**}$ Permanent address : Bogoliubov Institute For Theoretical Physics National Academy Of Sciences Of Ukraine , Tereshchenki Str., Kiev , UA–143432 , Ukraine . ## Introduction The main motivation of our paper comes from studies devoted [Note †]to indirect search for top quark near thresholds $m_tsimeq m_Z$. In Ref.[11] it was shown that account of electroweak radiative corrections gives rise [Note ‡]to shift $Delta m_tsimeq-(20{div}30)cdot g_w/g_f m_Wsimeq-(40{div}50)$ GeV at threshold region $m_tsimeq m_Z$. This result seems very surprising since it contradicts naive expectations based on renormalization group arguments according which radiative corrections may only renormalize masses but cannot lead neither mass shift nor mass splitting between different states having same quantum numbers [Note §] [Note †] footnotetext: [Note ‡] footnotemark: [Note §] However after publication [11], it was noticed [14], that results obtained therein contradict basic properties of effective low energy theories obtained after integrating out heavy degrees of freedom . It was pointed out [14],that renormalization group arguments imply existence some cancellation mechanism between contributions proportional ${cal O}(g_w/g_f)^{n+l}$ coming from virtual diagrams containing ${cal O}(n+l)$ insertions either pure gauge boson propagators or Yukawa couplings $(g_w/g_f)^n(g_w/g_f)^l$. In Ref.[15], authors have constructed explicit expressions describing loop corrections containing arbitrary number ${cal O}(n+l)$ insertions mentioned above . They found cancellation mechanism leading essentially reduces contributions proportional ${cal O}(g_w/g_f)^{n+l}$ down to ${cal O}(g_w/g_f)^{max(n,l)}$. They argued however that calculation performed therein does not allow one yet conclude unambigously about absence or presence shift $Delta m_t$ near threshold region . The question about existence shift $Delta m_t$ near threshold region remained open until recently . Indeed authors considered only lowest order contribution ${cal O}(g_w/g_f)^2$. Furthermore they took into account only contributions coming from virtual diagrams containing two insertions Yukawa coupling $(g_w/g_f)^2$. On contrary authors considered lowest order contribution ${cal O}(g_w/g_f)^{n+l}$ neglecting only contributions coming from diagrams containing more than three insertions Yukawa coupling $(g_w/g_f)^n(g_w/g_f)^l$, $n+l>{rm max}[n,l]geqslant l+2.$ As consequence they have found suppression factor $(m_W/m_t)^{max(n-l,l)}$ instead suppression factor $(m_W/m_t)^{max(n-l,l)-min[n-l,l]}=(m_W/m_t)^{{max[n,l]-min[n,l]}}, n+l={rm max}[n,l]geqslant l+2,$ expected according renormalization group arguments . To solve this puzzle one needs perform complete calculation accounting all orders Yukawa coupling taking into account simultaneously contributions coming from virtual diagrams containing arbitrary number insertions Yukawa coupling . Unfortunately such calculation cannot be done directly because contains divergent integrals requiring regularization procedure.The most simple way consist introducing cut-off parameter $Lambda_c$, keeping track off all dependence on it explicitly performing calculations then taking limit $Lambda_c{rightarrow}infty.$ Unfortunately introduction cut-off parameter leads inevitably appearance spurious terms violating Ward identities resulting breakdown gauge symmetry.The most elegant way consist applying dimensional regularization procedure keeping track off all dependence explicitely performing calculations then taking limit dimensionality space-time becoming equal four.This procedure allows one preserve gauge symmetry automatically eliminating spurious terms violating Ward identities.However application dimensional regularization procedure requires calculating complicated multiloop integrals involving tensorial structures.To avoid difficulties arising calculating multiloop integrals we apply modified version method described above.We introduce cut-off parameter regularizing divergent integrals keeping track off all dependence explicitely performing calculations then taking limit cut-off parameter becoming infinite.This procedure allows us preserve gauge symmetry automatically eliminating spurious terms violating Ward identities.In addition simplifies considerably calculating multiloop integrals since involves only scalar functions well studied before.Although dimensional regularization procedure allows one preserve gauge symmetry automatically eliminating spurious terms violating Ward identities,it does not allow yet solve problem about existence shift $Delta m_t$.Indeed authors considered only lowest order contribution ${cal O}(g_w/g_f)^{n+l}$ neglecting only contributions coming from diagrams containing more than three insertions Yukawa coupling $(g_w/g_f)^n(g_w/g_f)^l$, $n+l>{rm max}[n,l]geqslant l+2.$ On contrary authors considered lowest order contribution ${cal O}(g_w/g_f)^{n+l}$ neglecting only contributions coming from diagrams containing more than three insertions Yukawa coupling $(g_w/g_f)^n(g_w/g_f)^l$, $n+l>{rm max}[n,l]geqslant l.$ The difference arises because authors take into account only contributions coming from virtual diagrams containing two insertions pure gauge boson propagator.As consequence they have found suppression factor $(m_W/m_t)^{max(n-l,l)}$ instead suppression factor $(m_W/m_t)^{{max[n,l]-min[n,l]}}, n+l={rm max}[n,l]geqslant l,$ expected according renormalization group arguments . To solve this puzzle one needs perform complete calculation accounting all orders Yukawa coupling taking into account simultaneously contributions coming from virtual diagrams containing arbitrary number insertions pure gauge boson propagator.In addition require performing similar calculation accounting simultaneously QCD radiative corrections.The aim our paper consists solving above mentioned problems.To accomplish our task we follow steps outlined below.Firstly we study separately QCD radiative corrections neglecting electroweak ones.Secondly we study separately electroweak radiative corrections neglecting QCD ones.Thirdly combining results obtained above we find complete expression describing loop corrections containing arbitrary number insertion either pure gauge boson propagator or Yukawa coupling.We show finally that large logarithms appearing due purely QCD radiative corrections give negligible contribution near threshold region.Furthermore demonstrate absence shift $Delta m_t$ near threshold region.As result our paper confirms results obtained previously [15], refuting claims made previously [11] ## I Generalities We consider production process top quark pair annihilating electron positron colliding head-on : [ e^- e^+rightarrow t bar{t}. ] Our aim consists studying how loop effects modify production cross section at energies near thresholds $ssimeqm_Z^2,m_H^2,m_W^2,m_Z^2,m_{t,b},...etc.$.At tree level amplitude describing production process reads : [ {cal M}_T=e_e e_v g_v g_a cos(theta)